In a barrier potential with sections: I: V(x)=0 (x<-a), II:V(x)=V (-a<x<a) and III:V(x)=0 (a<x) you can write the solution in this form:(adsbygoogle = window.adsbygoogle || []).push({});

Ψ(x)=Ae^(ikx)+Be^(-ikx) (x<-a)

Ψ(x)=Ce^(ik'x)+De^(-ik'x) (-a<x<a)

Ψ(x)=Ee^(ikx) (a<x)

and with boundary conditions solve,

but why do you can write this solution in this form:

Ψ(x)=Ae^(ikx)+DAR^e(-ikx) (x<-a)

Ψ(x)=ACe^(ik'x)+AD^(-ik'x) (-a<x<a)

Ψ(x)=ATe^(ikx) (a<x)

with R reflection coefficient and T transmission coefficient

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# I Why can you write the solution in this form?

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